There is no universal special logo for a restaurant that composts.
You can see the Indigo airline emblem on it's wikipedia page here.
indigo
Verizon bought the rights to it from the government and then removed it, so the only indigo left would be in their logo.
Chili's
italian
I think that you are looking for Jamba Juice (jambajuice.com)
Jamba Juice
Ruby tuesday
Hardee's
ARBY'S
Dunkin donuts